AP Physics Practice Exam #6 Name: Hour: Practice Exam #6 Practice Exam Scoring Instructions: Each practice exam will be administered in class under official AP testing conditions. If absent, you are on the honor system to adhere to AP rules about equation sheets, calculators, and time. Your homework for each practice exam: (1) score it using the scoring key provided, (2) thoroughly correct all errors, (3) add the points earned for correcting errors and compute the total score below. Each practice exam, corrected, with the score sheet (below) filled out, is due Tuesday, May 12, 2015. Round all scores to the nearest 0.1 pt. Score Sheet Multiple Choice (35 Q's) x1 = Number of MC Q’s Correct (max. 35) (max. 35) x 0.8 = Number of MC Q’s Corrected (and mostly to fully understood) Special Instructions (This test only): Take this test in 45 minutes. Afterwards go to the following link, watch the answers and explanations on this 63-minute video: http://www.youtube.com/watch?v=C1D_QrVi_kM If this link doesn’t work, go to YouTube and search the following: 1998 AP Physics C Mechanics multiple choice solutions Total Score / Practice Exam 6 (round scores to the nearest 0.1) Practice Exam #6 – Page 1 /35 AP Physics Practice Exam #6 Name: Practice Exam #6 – Page 2 Hour: Practice Exam #6 AP Physics 1. Name: Hour: A force F is exerted by a broom handle on the head of the broom, which has a mass m. The handle is at an angle to the horizontal, as shown below. The work done by the force on the head of the broom as it moves a distance d across a horizontal floor is [1998/1] (A) 𝐹𝑑 sin 𝜃 (B) 𝐹𝑑 cos 𝜃 (C) 𝐹𝑚 cos 𝜃 (D) 𝐹𝑚 tan 𝜃 (E) 𝐹𝑚𝑑 sin 𝜃 _______________________________________________________________________________________________________________________________ 2. The velocity of a projectile at launch has a horizontal component 𝑣ℎ and a vertical component 𝑣𝑣 Air resistance is negligible. When the projectile is at the highest point of its trajectory, which of the following show the vertical and horizontal components of its velocity and the vertical component of its acceleration? [1998/2] Vertical Horizontal Velocity Velocity Vertical Acceleration (A) 𝑣𝑣 𝑣ℎ 0 (B) 𝑣𝑣 0 0 (C) 0 𝑣ℎ 0 (D) 0 0 𝑔 (E) 0 𝑣ℎ 𝑔 _______________________________________________________________________________________________________________________________ 3. The graph above shows the velocity v as a function of time t for an object moving in a straight line. Which of the following graphs shows the corresponding displacement x as a function of time t for the same time interval? [1998/3] Practice Exam #6 – Page 3 AP Physics 4. Practice Exam #6 Name: Hour: The position of a toy locomotive moving on a straight track along the 𝑥-axis is given by the equation 𝑥 = 𝑡 3 − 6𝑡 2 + 9𝑡 , where 𝑥 is in meters and 𝑡 is in seconds. The net force on the locomotive is equal to zero when t is equal to [1998/4] (A) zero (B) 2 s (C) 3 s (D) 4 s (E) 5 s _______________________________________________________________________________________________________________________________ 5. A system of two wheels fixed to each other is free to rotate about a frictionless axis through the common center of the wheels and perpendicular to the page. Four forces are exerted tangentially to the rims of the wheels, as shown above. The magnitude of the net torque on the system about the axis is [1998/5] (A) zero (B) 𝐹𝑅 (C) 2 𝐹𝑅 (D) 5 𝐹𝑅 (E) 14 𝐹𝑅 _______________________________________________________________________________________________________________________________ 6. A wheel of mass M and radius R rolls on a level surface without slipping. If the angular velocity of the wheel is 𝜔, what is its linear momentum ? [1998/6] (A) 𝑀𝜔𝑅 (B) 𝑀𝜔2 𝑅 (C) 𝑀𝜔𝑅 2 (D) 𝑀𝜔2 𝑅2 /2 (E) Zero _______________________________________________________________________________________________________________________________ Questions 7-8 Refer to a ball that is tossed straight up from the surface of a small, spherical asteroid with no atmosphere. The ball rises to a height equal to the asteroid's radius and then falls straight down toward the surface of the asteroid. 7. [1998/7] What forces, if any, act on the ball while it is on the way up? (A) (B) (C) (D) Only a decreasing gravitational force that acts downward Only an increasing gravitational force that acts downward Only a constant gravitational force that acts downward Both a constant gravitational force that acts downward and a decreasing force that acts upward (E) No forces act on the ball. Practice Exam #6 – Page 4 Practice Exam #6 AP Physics 8. Name: Hour: The acceleration of the ball at the top of its path is [1998/8] (A) at its maximum value for the ball's flight (B) equal to the acceleration at the surface of the asteroid (C) equal to one-half the acceleration at the surface of the asteroid (D) equal to one-fourth the acceleration at the surface of the asteroid (E) zero _______________________________________________________________________________________________________________________________ 9. The equation of motion of a simple harmonic oscillator is 𝑑2 /𝑑𝑡 2 = −9𝑥 , where 𝑥 is displacement and 𝑡 is time. The period of oscillation is [1998/9] (A) 6𝜋 (B) 9/2𝜋 (C) 3/2𝜋 (D) 2𝜋/3 (E) 2𝜋/9 _______________________________________________________________________________________________________________________________ 10. A pendulum with a period of 1 second on Earth, where the acceleration due to gravity is g, is taken to another planet, where its period is 2 seconds. The acceleration due to gravity on the other planet is most nearly [1998/10] (A) 𝑔/4 (B) 𝑔/2 (C) 𝑔 (D) 2𝑔 (E) 4𝑔 _______________________________________________________________________________________________________________________________ 11. A satellite of mass M moves in a circular orbit of radius R with constant speed v. True statements about this satellite include which of the following? [1998/11] I. Its angular speed is 𝑣/𝑅. II. Its tangential acceleration is zero. III. The magnitude of its centripetal acceleration is constant. (A) (B) (C) (D) (E) I only II only I and III only II and III only I, II, and III Practice Exam #6 – Page 5 Practice Exam #6 AP Physics 12. Name: Hour: The graph above shows the force on an object of mass M as a function of time. For the time interval 0 to 4 s, the total change in the momentum of the object is [1998/12] (A) 40 kgm/s (B) 20 kgm/s (C) 0 kgm/s (D) −20 kgm/s (E) indeterminable unless the mass M of the object is known _______________________________________________________________________________________________________________________________ 13. As shown in the top view above, a disc of mass m is moving horizontally to the right with speed 𝑣 on a table with negligible friction when it collides with a second disc of mass 2m The second disc is moving horizontally to the right with speed 𝑣/2 at the moment of impact. The two discs stick together upon impact. The speed of the composite body immediately after the collision is [1998/13] (A) 𝑣/3 (B) 𝑣/2 (C) 2𝑣/3 (D) 3𝑣/2 (E) 2𝑣 _______________________________________________________________________________________________________________________________ Questions 14-15 A spring has a force constant of 100 N/m and an unstretched length of 0.07 m. One end is attached to a post that is free to rotate in the center of a smooth table, as shown in the top view above. The other end is attached to a 1 kg disc moving in uniform circular motion on the table, which stretches the spring by 0.03 m. Friction is negligible. 14. [1998/14] (A) (B) (C) (D) (E) What is the centripetal force on the disc? 0.3 N 3N 10 N 300 N 1,000 N Practice Exam #6 – Page 6 Practice Exam #6 AP Physics 15. [1998/15] Name: Hour: What is the work done on the disc by the spring during one full circle? (A) 0 J (B) 94 J (C) 186 J (D) 314 J (E) 628 J _______________________________________________________________________________________________________________________________ Questions 16-17 refer to the following graph, which represents a hypothetical potential energy curve for a particle of mass m. 16. 17. [1998/16] If the particle is released from rest at position 𝑟0 , its speed at position 2𝑟0 is most nearly (A) √ 8𝑈0 (B) √ 6𝑈0 (C) √ 4𝑈0 (D) √ 2𝑈0 (E) √ 𝑈0 𝑚 𝑚 𝑚 𝑚 𝑚 If the potential energy function is given by U(r) = br-3/2 + c, where b and c are constants, which of the following is an expression for the force on the particle? [1998/17] (A) (B) (C) 3𝑏 −5/2 𝑟 2 3𝑏 −1/2 𝑟 2 3 −1/2 𝑟 2 (D) 2𝑏𝑟 −1/2 + 𝑐𝑟 (E) 2𝑏 −5/2 𝑟 + 𝑐𝑟 5 Practice Exam #6 – Page 7 AP Physics 18. Practice Exam #6 Name: Hour: A frictionless pendulum of length 3 m swings with an amplitude of 10°. At its maximum displacement, the potential energy of the pendulum is 10 J. What is the kinetic energy of the pendulum when its potential energy is 5 J ? [1998/18] (A) 3.3 J (B) 5 J (C) 6.7 J (D) 10 J (E) 15 J _______________________________________________________________________________________________________________________________ 19. A descending elevator of mass 1,000 kg is uniformly decelerated to rest over a distance of 8 m by a cable in which the tension is 11,000 N. The speed 𝑣𝑖 of the elevator at the beginning of the 8 m descent is most nearly [1998/19] (A) 4 m/s (B) 10 m/s (C) 13 m/s (D) 16 m/s (E) 21 m/s _______________________________________________________________________________________________________________________________ 20. Two identical stars, a fixed distance D apart, revolve in a circle about their mutual center of mass, as shown above. Each star has mass M and speed v. G is the universal gravitational constant. Which of the following is a correct relationship among these quantities? [1998/20] (A) 𝑣 2 = 𝐺𝑀/𝐷 (B) 𝑣 2 = 𝐺𝑀/2𝐷 (C) 𝑣 2 = 𝐺𝑀/𝐷 2 (D) 𝑣 2 = 𝑀𝐺𝐷 (E) 𝑣 2 = 2𝐺𝑀2 /𝐷 Practice Exam #6 – Page 8 Practice Exam #6 AP Physics Name: Hour: Questions 21-22 A block of mass m is accelerated across a rough surface by a force of magnitude F that is exerted at an angle 𝜙 with the horizontal, as shown above. The frictional force on the block exerted by the surface has magnitude f. 21. [1998/21] What is the acceleration of the block? (A) 𝐹/𝑚 (B) 𝐹 cos 𝜙/𝑚 (C) (𝐹 − 𝑓)/𝑚 (D) (𝐹 cos 𝜙 − 𝑓)/𝑚 (E) (𝐹 sin 𝜙 − 𝑚𝑔)/𝑚 22. [1998/22] What is the coefficient of friction between the block and the surface? (A) 𝑓/𝑚𝑔 (B) 𝑚𝑔/𝑓 (C) (𝑚𝑔 − 𝐹 cos 𝜙)/𝑓 (D) 𝑓/(𝑚𝑔 − 𝐹 cos 𝜙) (E) 𝑓/(𝑚𝑔 − 𝐹 sin 𝜙) _______________________________________________________________________________________________________________________________ 23. [1998/23] This question was omitted and not counted when the exam was scored. _______________________________________________________________________________________________________________________________ 24. Two people are initially standing still on frictionless ice. They push on each other so that one person, of mass 120 kg, moves to the left at 2 m/s, while the other person, of mass 80 kg, moves to the right at 3 m/s. What is the velocity of their center of mass? [1998/24] (A) (B) (C) (D) (E) Zero 0.5 m/s to the left 1 m/s to the right 2.4 m/s to the left 2.5 m/s to the right Practice Exam #6 – Page 9 AP Physics 25. Practice Exam #6 Name: Hour: A figure of a dancer on a music box moves counterclockwise at constant speed around the path shown above. The path is such that the lengths of its segments, PQ, QR, RS, and SP, are equal. Arcs QR and SP are semicircles. Which of the following best represents the magnitude of the dancer's acceleration as a function of time t during one trip around the path, beginning at point P ? [1998/25] Practice Exam #6 – Page 10 Practice Exam #6 AP Physics 26. Name: Hour: A target T lies flat on the ground 3 m from the side of a building that is 10 m tall, as shown above. A student rolls a ball off the horizontal roof of the building in the direction of the target. Air resistance is negligible. The horizontal speed with which the ball must leave the roof if it is to strike the target is most nearly [1998/26] (A) 3/10 m/s (B) √2 m/s (C) 3 √2 m/s (D) 3 m/s 5 (E) 10√3 m/s _______________________________________________________________________________________________________________________________ 27. To stretch a certain nonlinear spring by an amount x requires a force 𝐹 given by = 40𝑥 − 6𝑥 2 , where 𝐹 is in newtons and 𝑥 is in meters. What is the change in potential energy when the spring is stretched 2 meters from its equilibrium position? [1998/27] (A) 16 J (B) 28 J (C) 56 J (D) 64 J (E) 80 J _______________________________________________________________________________________________________________________________ 28. When a block slides a certain distance down an incline, the work done by gravity is 300 J. What is the work done by gravity if this block slides the same distance up the incline? [1998/28] (A) 300 J (B) Zero (C) −300 J (D) It cannot be determined without knowing the distance the block slides. (E) It cannot be determined without knowing the coefficient of friction. _______________________________________________________________________________________________________________________________ 29. A particle moves in the 𝑥𝑦-plane with coordinates given by 𝑥 = 𝐴 cos 𝜔𝑡 and 𝑦 = 𝐴 sin 𝜔𝑡 , where A = 1.5 meters and 𝜔 = 2.0 radians per second. What is the magnitude of the particle's acceleration? [1998/29] (A) (B) (C) (D) (E) Zero 1.3 m/s2 3.0 m/s2 4.5 m/s2 6.0 m/s2 Practice Exam #6 – Page 11 AP Physics 30. Practice Exam #6 Name: Hour: For the wheel-and-axle system shown above, which of the following expresses the condition required for the system to be in static equilibrium? [1998/30] (A) 𝑚1 = 𝑚2 (B) 𝑎𝑚1 = 𝑏𝑚2 (C) 𝑎𝑚2 = 𝑏𝑚1 (D) 𝑎2 𝑚1 = 𝑏 2 𝑚2 (E) 𝑏 2 𝑚1 = 𝑎2 𝑚2 _______________________________________________________________________________________________________________________________ 31. An object having an initial momentum that may be represented by the vector above strikes an object that is initially at rest. Which of the following sets of vectors may represent the momenta of the two objects after the collision? [1998/31] (A) (B) (C) (D) (E) Practice Exam #6 – Page 12 Practice Exam #6 AP Physics Name: Hour: Questions 32-33 A wheel with rotational inertia I is mounted on a fixed, frictionless axle. The angular speed 𝜔 of the wheel is increased from zero to 𝜔𝑓 in a time interval T. 32. (A) (B) (C) (D) (E) 33. What is the average net torque on the wheel during this time interval? [1998/32] 𝜔𝑓 𝑇 𝜔𝑓 𝑇2 𝐼𝜔𝑓2 𝑇 𝐼𝜔𝑓 𝑇2 𝐼𝜔𝑓 𝑇 [1998/33] (A) (B) (C) (D) (E) What is the average power input to the wheel during this time interval? 𝐼𝜔𝑓 2𝑇 𝐼𝜔𝑓2 2𝑇 𝐼𝜔𝑓2 2𝑇 2 𝐼 2 𝜔𝑓 2𝑇 2 𝐼 2 𝜔𝑓2 2𝑇 2 _______________________________________________________________________________________________________________________________ 34. An object is released from rest at time t = 0 and falls through the air, which exerts a resistive force such that the acceleration a of the object is given by 𝑎 = 𝑔 − 𝑏𝑣 , where 𝑣 is the object's speed and 𝑏 is a constant. If limiting cases for large and small values of t are considered, which of the following is a possible expression for the speed of the object as an explicit function of time? [1998/34] (A) 𝑣 = 𝑔(1 − 𝑒 −𝑏𝑡 )/𝑏 (B) (C) (D) (E) 𝑣 𝑣 𝑣 𝑣 = (𝑔𝑒 ℎ𝑡 )/𝑏 = 𝑔𝑡 − 𝑏𝑡 2 = (𝑔 + 𝑎)𝑡/𝑏 = 𝑣0 + 𝑔𝑡 , 𝑣0 ≠ 0 Practice Exam #6 – Page 13 Practice Exam #6 AP Physics 35. Name: Hour: An ideal massless spring is fixed to the wall at one end, as shown above. A block of mass M attached to the other end of the spring oscillates with amplitude A on a frictionless, horizontal surface. The maximum speed of the block is 𝑣𝑚 . The force constant of the spring is [1998/35] (A) (B) (C) (D) (E) 𝑀𝑔 𝐴 𝑀𝑔𝑣𝑚 2𝐴 2 𝑀𝑣𝑚 2𝐴 2 𝑀𝑣𝑚 𝐴2 2 𝑀𝑣𝑚 2𝐴2 _______________________________________________________________________________________________________________________________ End of MC Section Answer Key — See Instructions on page 1. Practice Exam #6 – Page 14

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